Finite Group Databasebeta

← Prev (#28398972) Next (#28398974) →

C2×C4×C8×D113 #28398973

order14464
isoclinismisoclinic class of D113
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D113

Splittings

FittingC2×C4×C8×C113 ⋊ C2
derived, SylowC113 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D113
commutator, hypocenterC113C22×C4×C8
FrattiniC2×C4C23×D113
FittingC2×C4×C8×C113C2
socleC23×C113C22×C4
prime radicalC23×D113C2×C4
cosocleC2×C4×C113C24
LCSG ▷ C113
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12909);